Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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        <div xml:id="echoid-div33" type="section" level="1" n="30">
          <head xml:id="echoid-head52" xml:space="preserve">SECTIO PRIMA</head>
          <head xml:id="echoid-head53" xml:space="preserve">Continens propoſitiones I. II. & III. Apollonij.</head>
          <head xml:id="echoid-head54" xml:space="preserve">PROPOSITIO I.</head>
          <p>
            <s xml:id="echoid-s838" xml:space="preserve">Si ex centro D ſectionis A B (habentis centrum) egrediatur
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            linea recta D F H bifariam diuidens A E erectum illius axis,
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            quod ſit perpendiculare ſuper axim C A G, ſecans axis ordina-
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            tionem B G I; </s>
            <s xml:id="echoid-s839" xml:space="preserve">vtiquè dimidium illius ordinationis, videlicet B
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            G, poterit duplum plani, quod producit illa linea cum axi in-
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            ter erectum, & </s>
            <s xml:id="echoid-s840" xml:space="preserve">illam ordinationem, nempè duplum A G H F.</s>
            <s xml:id="echoid-s841" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s842" xml:space="preserve">QVia B G poteſt comparatum applicatum ad abſciſſam A G, & </s>
            <s xml:id="echoid-s843" xml:space="preserve">pla-
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              <note position="left" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">a</note>
            num G F dimidium eſt illius comparati; </s>
            <s xml:id="echoid-s844" xml:space="preserve">ergò B G poterit duplum
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              <note position="left" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve">b</note>
            plani G F; </s>
            <s xml:id="echoid-s845" xml:space="preserve">& </s>
            <s xml:id="echoid-s846" xml:space="preserve">hoc erat oſtendendum.</s>
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          <head xml:id="echoid-head55" xml:space="preserve">PROPOS. II.</head>
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          <p>
            <s xml:id="echoid-s848" xml:space="preserve">PAritèr quoquè oſtendetur, ſi potens
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            tranſierit per centrum ellipſis, quod
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            B G poterit duplum trianguli A F G.</s>
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